Astronomy & Astrophysics manuscript no. HD172555_v7_arxiv c ESO 2018 August 15, 2018
Detection of scattered light from the hot dust in HD 172555 ? ?? N. Engler1, H.M. Schmid1, S.P. Quanz1, H. Avenhaus2, and A. Bazzon1
1 ETH Zurich, Institute for Particle Physics and Astrophysics, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland e-mail: [email protected] 2 Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
Received ...; accepted ...
ABSTRACT
Context. Debris disks or belts are important signposts for the presence of colliding planetesimals and, therefore, for ongoing planet formation and evolution processes in young planetary systems. Imaging of debris material at small separations from the star is very challenging but provides valuable insights into the spatial distribution of so-called hot dust produced by solid bodies located in or near the habitable zone. We report the first detection of scattered light from the hot dust around the nearby (d = 28.33 pc) A star HD 172555. Aims. We want to constrain the geometric structure of the detected debris disk using polarimetric differential imaging (PDI) with a spatial resolution of 25 mas and an inner working angle of about 0.100. Methods. We measured the polarized light of HD 172555, with SPHERE-ZIMPOL, in the very broad band (VBB) or RI filter 00 00 (λc = 735 nm, ∆λ = 290 nm) for the projected separations between 0.08 (2.3 au) and 0.77 (22 au). We constrained the disk parameters by fitting models for scattering of an optically thin dust disk taking the limited spatial resolution and coronagraphic attenuation of our data into account. Results. The geometric structure of the disk in polarized light shows roughly the same orientation and outer extent as obtained from thermal emission at 18 µm. Our image indicates the presence of a strongly inclined (i ≈ 103.5◦), roughly axisymmetric dust belt with an outer radius in the range between 0.300 (8.5 au) and 0.400 (11.3 au). An inner disk edge is not detected in the −5 data. We derive a lower limit for the polarized flux contrast ratio for the disk of (Fpol)disk/F∗ > (6.2±0.6)·10 in the VBB filter. This ratio is small, only ∼9 %, when compared to the fractional infrared flux excess (≈ 7.2 · 10−4). The model simulations show that more polarized light could be produced by the dust located inside ≈ 2 au, which cannot be detected with the instrument configuration used. Conclusions. Our data confirm previous infrared imaging and provide a higher resolution map of the system, which could be further improved with future observations. Key words. Planetary systems – Scattering – Stars: individual object: HD 172555, HR 7012, HIP 92024 – Techniques: high angular resolution, polarimetric
1. Introduction (e.g., Moerchen et al. 2010; Schneider et al. 2014; Choquet et al. 2016; Olofsson et al. 2016; Bonnefoy et al. 2017). Young stars are often surrounded by circumstellar dust debris disks or rings. These consist of solid bodies, such as planetes- In the absence of imaging data, the location of the bulk of imals and comets, as well as large amounts of dust and small dust in the system can be inferred from the grain temperature amounts of gas. Small dust grains with a broad size distribu- derived by SED modeling. Based on modeling results, most tion are generated in steady collisions of solid bodies and per- debris disks have been found to harbor warm dust, meaning haps by the evaporation of comets. Debris disks are usually that the temperature of small grains lies between 100 and recognized by infrared (IR) excess on top of the spectral en- approximately 300 K (e.g., Moór et al. 2006; Trilling et al. ergy distribution (SED) of the stellar photosphere because of 2008; Chen et al. 2011; Morales et al. 2011). Cold debris the thermal emission of the heated dust grains (see, e.g., Wyatt reside far away from the host star where their temperature 2008; Matthews et al. 2014, for a review). In scattered light, does not exceed 100 K. The prominent analogs to warm and debris disks are usually very faint, i.e., > 103 times fainter cold dust belts are the main asteroid belt at 2-3.5 au and the arXiv:1808.04373v1 [astro-ph.EP] 13 Aug 2018 than the host star, and therefore they are difficult to image. To Kuiper belt between 30 and 48 au in the solar system (Wy- date, several dozen debris disks have been spatially resolved att 2008). Aside from this, several stars with hot disks have in various wavelength bands, from visible to millimeter, using been found (Wyatt et al. 2007a; Fujiwara et al. 2009) based various space and ground-based telescopes. These data pro- on the IR excess with an estimate temperature above 300 K. vide important constraints on the debris disk morphologies The stars that possess hot dust are very interesting targets be- cause the submicron-sized grains at a small small distance ? Based on data collected at the European Southern Observatory, from a star could be a signpost for transient collision events. Chile under program 095.C-192 HD 172555 (HIP 92024, HR 7012) is one of the most stud- ?? The reduced images as FITS files are available in electronic form ied objects among these special stellar systems (Cote 1987; at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) Schütz et al. 2005; Chen et al. 2006; Wyatt et al. 2007b; Lisse or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/ et al. 2009; Smith et al. 2012; Riviere-Marichalar et al. 2012;
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Johnson et al. 2012; Kiefer et al. 2014; Wilson et al. 2016; 2. Observations Grady et al. 2018). Observations of HD 172555 were taken in service or queue HD 172555 is a V = 4.8m, A7V star (Høg et al. 2000; Gray mode during six runs in 2015 as part of the open time pro- et al. 2006) at a distance of 28.33 ± 0.19 pc (Gaia Collabo- gram 095.C-192 using ZIMPOL, the visual subsystem of the ration 2016) and a member of the β Pictoris moving group. SPHERE (Spectro-Polarimetric High-contrast Exoplanet RE- The deduced age for the group is 23 ± 3 Myr (Mamajek & search) instrument. The SPHERE instrument was developed Bell 2014). HD 172555 has a K5Ve low mass companion for high contrast observations in the visual and near-IR spec- 00 CD-64 1208, separated by more than 2000 au or 71.4 (Tor- tral range and includes an extreme adaptive optics (AO) sys- res et al. 2006). The Infrared Astronomical Satellite (IRAS) tem and three focal plane instruments for differential imaging identified HD 172555 as a Vega-like star that has a large IR (Beuzit et al. 2008; Kasper et al. 2012; Dohlen et al. 2006; excess with an effective temperature of 290 K (Cote 1987). Fusco et al. 2014, Schmid et al. 2018, submitted). Mid-infrared (mid-IR) spectroscopy from the ground (Schütz et al. 2005) and 5.5-35 µm spectroscopy obtained with the The ZIMPOL polarimetry is based on a modulation- Spitzer Infrared Spectrograph (IRS) show very pronounced demodulation technique and our observations of HD 172555 SiO features (Chen et al. 2006, their Fig. 2(d)) indicating in the VBB filter were carried out in the fast modulation large amounts of submicron sized crystalline silicate grains mode using field stabilization, which is also known as the with high temperatures (> 300 K). Lisse et al. (2009) pro- P2 derotator mode. The ZIMPOL modulation technique mea- posed, based on the spectral analysis of mineral features, that sures the opposite polarization states of incoming light quasi- the IR-excess emission originates from a giant collision of simultaneously and with the same pixels such that differential large rocky planetesimals similar to the event that could have aberrations between I⊥ and Ik are minimized. Fast modulation created the Earth-Moon system. means a polarimetric cycle frequency of 967.5 Hz, which is obtained with a ferro-electric liquid crystal (FLC) and a polar- Until now, only one resolved image of the HD 172555 ization beam splitter in front of the demodulating CCD detec- − debris disk existed that was obtained in the Qa band (λc = tor. The high detector gain of 10.5 e /ADU allows broadband 18.30 µm, ∆λ = 1.52 µm; hereafter Q band) with TReCS observations with high photon rates without pixel saturation (Thermal-Region Camera Spectrograph) at Gemini South and ensures high sensitivity at small angular separations at the telescope and described by Smith et al. (2012). They detected expense of a relative high readout noise. The ZIMPOL VBB extended emission after subtraction of a standard star point or RI filter used (λc = 735 nm, ∆λ = 290 nm) covers the spread function (PSF), which is consistent with an inclined R band and I band. Polarimetric data were taken in corona- disk with an orientation of the major axis of θ = 120◦, an graphic mode using the Lyot coronagraph V_CLC_MT_WF inclination of ≈ 75◦, and a disk outer radius of 8 au. In Si-5 with a diameter of 155 mas. The mask is semi-transparent filter (λc = 11.66 µm, ∆λ = 1.13 µm; hereafter N band) data, such that the central star is visible as faint PSF in the mid- the disk was not detected. Combining these results with the dle of attenuation region if the stellar PSF is of good quality visibility functions measured with the MID-infrared Interfer- (good AO corrections) and well centered on the mask. Short ometric instrument (MIDI), Smith et al. (2012) concluded that flux calibrations (the star was offset from the coronagraphic the warm dust radiating at ∼10 µm is located inside 8 au from mask) with detector integration time (DIT) of 1.2 s and total the star or inside the detected 18 µm emission. exposure time of 14.4 s were also taken in each run using the neutral density filter ND2 with a transmission of about 0.87% The proximity of the host star and strong excess in the for the VBB filter to avoid heavy saturation of the PSF peak. · −4 mid-IR (LIR/L∗ = 7.2 10 ; Mittal et al. 2015) from hot dust, The ZIMPOL instrument is equipped with two detec- makes HD 172555 an excellent, yet challenging, object for tors/cameras, cam1 and cam2, which both have essentially the the search of scattered light. In this paper, we report the first same field of view of 3.600 ×3.600. The format of the processed detection of scattered light from the hot debris disk around frame is 1024 × 1024 pixels, where one pixel corresponds to HD 172555 with polarimetric differential imaging (PDI). 3.6 × 3.6 mas on sky. The spatial resolution of our data pro- We present the PDI data from 2015 taken with ZIMPOL vided by the AO-system is about 25 mas. (Zurich IMaging POLarimeter; Schmid et al. 2018, submit- The HD 172555 data were taken at three different sky ori- ted) at the Very Large Telescope (VLT) in Chile. The ZIM- entations on the CCD detectors with position angle (PA) off- POL instrument provides high contrast imaging polarimetry, sets of 0◦, 60◦ and 120◦ with respect to sky north. For each coronagraphy with a small inner working angle of ∼0.100, and field orientation, eight polarimetric QU cycles were recorded high spatial resolution of ∼25 mas. The next section presents consisting each of four consecutive exposures of the Stokes the available data together with a brief description of the in- linear polarization parameters +Q, −Q, +U and −U using strument. Section 3 describes the data reduction and Section half-wave plate (HWP) offset angles of 0◦, 45◦, 22.5◦, and 4 the obtained results. Section 5 includes analysis of the ob- 67.5◦, respectively. For each exposure, eight frames with DIT served disk morphology and photometry. For the interpreta- of 10 s were taken and this yields a total integration of 10 s × tion of the data we calculated three-dimensional (3D) disk 8 frames × 4 exposures × 8 cycles or ∼42.7 minutes. Because models for spatial distribution of dust to put constraints on the of a timing error in the control law (see Maire et al. 2016) geometric parameters of the disk and to estimate the flux can- of the derotator during the first three runs performed in June cellation effects in the Stokes Q and U parameters. In Sect. 6, 2015, the program was re-executed in August and Septem- we compare our results with previous TReCS and MIDI ob- ber 2015. However, it turned out that this timing error was servations (Smith et al. 2012). We also investigate the pos- so small, that it does not significantly affect the imaging of sible presence of a very compact dust scattering component an extended source at small separation. Therefore none of the that would not be detectable in our data. We conclude and six disk observations for HD 172555 are degraded by this ef- summarize our findings in Sect. 7. fect. All our deep polarimetric observations of HD 172555
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Table 1. Log of observations with the atmospheric conditions for each run.
Date Observation Field Observing conditions (on average) identification1 offset [◦] Airmass Seeing ["] Coherence time [ms] Wind speed [ms−1] 2015-06-21 OBS172_0004-0036 0 1.32 1.39 1.1 7.9 2015-06-26 OBS177_0010-0042 120 1.31 0.78 3.5 6.7 2015-07-12 OBS193_0049-0081 60 1.33 1.41 0.9 1.8 2015-09-06 OBS249_0028-0060 0 1.35 0.93 3.8 9.0 2015-09-06 OBS249_0061-0094 60 1.47 1.11 3.4 8.7 2015-09-07 OBS250_0002-0034 120 1.55 2.01 1.0 16.1
Notes. (1) The observation identification corresponds to the fits-file header keyword “origname” without prefix “SPHERE_ZIMPOL_”. The first three digits give the day of the year followed by the four-digit observation number. Instrument setup for the deep imaging mode: Fast polarimetry, VBB filter, derotator mode P2, coronagraph V_CLC_MT_WF, and total exposure time for each run 42.7 min. Instrument setup for the flux calibration mode: Fast polarimetry, VBB filter, density filter ND2, derotator mode P2, and total exposure time for each run 14.4 s.
are listed in Table 1 together with the observing conditions, larimetry. Figure B.1 shows the Stokes I, Q, and U images which have an important impact on the data quality. of these data sets in comparison with the reduced data from the other observing runs that were affected by poor observing conditions. 3. Data reduction To have a higher S/N per resolution element, images were The data were reduced with the SPHERE-ZIMPOL data re- 8 × 8 (Fig. 1) binned for the data analysis and modeling. In duction pipeline developed at ETH Zurich. We applied very Fig. 2 we used a smaller binning (6×6) to preserve the spatial similar procedures as in Engler et al. (2017) using flux nor- information and to have a more detailed picture of the disk. malization before polarimetric combination of the data. For high contrast polarimetry at small separations from 4. Features in the reduced data the star an accurate centering and the correction of the ZIM- POL polarimetric beam-shift are important (Schmid et al. The top row of Figure 1 shows the main results of our data 2018, submitted). The stellar position behind the mask should reduction, i.e., the mean intensity or Stokes I, Stokes Qϕ, and be determined with a precision higher than 0.3 pixels, other- Uϕ images using all eight cycles of the best night. The second wise the final image shows strong offset residuals disturbing row shows the same for six out of eight cycles from the second the detection of a faint polarimetric signal. For the fine center- best night. The bottom row is the mean of these data. ing we fitted a 2D Gaussian function using a central subim- The quality of the data can be easily recognized in the age with a radius of eight pixels containing the stellar light coronagraphic intensity images. These images show, for the spot transmitted through a semitransparent coronagraphic fo- best night (top), a much weaker halo and a weaker speckle cal plane mask. ring at a separation of about r ≈ 0.3500 than for the second The output of the data reduction pipeline consists of im- best night (middle). For all other nights the disturbing light ages of the intensity or Stokes I and the Stokes Q and U halo and speckles from the central star are even stronger (see fluxes, where Q = I0 − I90 is positive for a linear polarization Fig. B.1). Also clearly visible in Fig. 1 is the rotated speckle in N-S-direction and U = I45 − I135 is positive for a polar- pattern in the top I image, which was taken with a field ori- ization in NE-SW direction. For the data analysis, we trans- entation of 120◦, with respect to the middle I image taken formed the Q and U images into a tangential or azimuthal without field orientation offset or 0◦. In the latter image two polarization images Qϕ and Uϕ, locally defined with respect strong quasi-static speckles from the AO system (indicated to the central light source. This transformation is useful for with white arrows) are located left and right from the central an optically thin circumstellar scattering region because the source on the speckle ring. The same speckles are rotated in ◦ polarization signal is mainly in the Qϕ component, while Uϕ the top image by 120 because of the applied field rotation. should be zero (e.g., Schmid et al. 2006, see also Appendix The Qϕ image from the best night in the top row shows a A). positive signal or tangential polarization for regions just ESE During the data reduction, it turned out that an accurate and WNW from the coronagraphic mask and some noisy fea- centering of our HD 172555 images is difficult and not possi- tures at the location of the two strong speckles. The corre- ble for a substantial portion of our data because several runs sponding Uϕ image is also noisy but shows no predominant suffered from mediocre atmospheric conditions with a see- extended feature as seen in Qϕ. The same ESE–WNW exten- 00 ing > 1 and therefore strongly reduced AO performance. sion is also present in the Qϕ image of the second best night, Because of this problem only data from the best night 177 but now the disturbing strong speckles are adding noise in the 00 (2015-06-26; see Table 1) with an average seeing of 0.78 E-W direction, particularly well visible in the Uϕ image. Be- and most data from the second best night 249 (2015-09-06) sides this, both Qϕ and Uϕ for the second best night show a with seeing of 0.9300 could be used for our high contrast po- quadrant pattern that is typical for a not perfectly corrected
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14 au
Fig. 1. Polarimetric differential imaging data of HD 172555 with the VBB filter (590-880 nm). The 8 × 8 binned images show polarized flux computed as Stokes I (left column), Qϕ (middle column), and Uϕ (right column) parameters. Top row: Observation OBS177_0010-0042 (see Table 1 for the observational conditions) data averaged over 8 QU cycles. Middle row: Observation OBS249_0028-0060 data averaged over 6 QU cycles. Bottom row: Average of the data presented in the top and middle rows. The position of the star is denoted by a yellow asterisk. White arrows point out quasi-static speckles from the AO system. In all images north is up and east is to the left. The color bars show the counts per binned pixel. component from the telescope polarization. The following sociated with instrumental effects, strongly supports an inter- analysis of the disk morphology and modeling are based on pretation that this is a real detection of the debris dust around the Qϕ image in the top row obtained under the best observing HD 172555. This is further supported by the fact that the ori- conditions because these data are the least affected by noise. entation and extent of the detected feature coincides at least roughly with the disk detection reported previously by Smith The fact that we see the same kind of extended feature et al. (2012) based on imaging in the mid-IR. in the ESE-WNW orientation in both data sets (from the best and second best nights), while other features can clearly be as-
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a
y N b E A B
x
0.2 ’’ 6 AU
Fig. 2. Qϕ image (a) and isophotal contours of polarized light intensity overlying the Qϕ image (b). The original data (OBS177_0010-0042) were 6 × 6 binned to highlight the disk shape and to reduce the photon noise level. The position of the star is indicated by a yellow asterisk. White brackets in the top panel show the boundaries of two rectangular areas where the counts were summed up to retrieve the total polarized flux of the disk (see Sect. 5.3). Image (b) is smoothed via a Gaussian kernel with σkernel = 3 px. The isophotal contours show levels of the surface brightness with approx. 25, 40, and 50 counts per binned pixel (from the lowest to the highest contour). Arrows "A" and "B" mark the location of the increased surface brightness, which could indicate the radius of the planetesimal belt. The x-axis coincides with the disk ◦ axis at estimated PA θdisk = 112 (see Sect. 5). The color bar shows the surface brightness in counts per binned pixel.
In our image there is a prominent bright spot located be- 5. Analysis low the coronagraphic mask. Most likely it is a spurious fea- ture originating from image jitter and the temporal leakage of 5.1. Disk position angle and morphology light of the central star from behind the coronagraphic mask. To determine the PA of the disk θdisk, we varied the posi- ◦ It is seen more particularly in 177 data set, which argues tion of the disk major axis in the range from θdisk = 105 ◦ ◦ against this being a real feature. to θdisk = 125 with a step of 0.5 . Each time the Qϕ image ◦ was rotated by θdisk − 90 clockwise to place the disk major axis horizontally and then we determined the difference be- tween the left side and the mirrored right side of the image. The minimum residual flux corresponding to the best match ◦ between disk sides is achieved at θdisk = 113.5 for the data A final remark on the data quality. Our data look noisy set from 2015-06-26 (night 177) and at PA = 116.5◦ for the and are affected by not well corrected instrumental effects. data set from 2015-09-06 (night 249). ◦ ◦ However, we note that the signals in the Qϕ and Uϕ images are We adopted the PA equal θdisk = 114 ±3 . This PA should at a very low level of 0.001 of the signal in the intensity frame be corrected for the ZIMPOL True North offset of −2◦, which −5 ◦ or the surface brightness in the Qϕ image is on the order 10 means the preprocessed image must be rotated by 2 clock- ◦ ◦ of the expected peak flux of the central star for a separation of wise. The final PA of the disk is, therefore, θdisk = 112 ± 3 < 0.3 arcsec. The detection of this faint target requires very north over east (NoE), where the indicated uncertainty in- high contrast polarimetry at small angular separation. Not all cludes associated systematic errors. For the following data ◦ instrumental effects are understood and can be calibrated at analysis, the Qϕ image was rotated by 24 clockwise, includ- this level of sensitivity yet. ing the correction for the True North offset, to place the disk
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00 00 Fig. 3. Radial polarized flux profile measured in the Qϕ image per 0.029 (∆x) × 0.290 (∆y) bin (red solid line) compared with profiles of the best-fitting models and background. The background above (green solid line) and below (light green dotted line) the disk midplane and the background in the Uϕ image (black solid line) are calculated as explained in Sect. 5. The upper limit is set for the polarized flux per bin for the disk regions beyond r = 0.5300. The arrows "A" and "B" point to the surface brightness peaks. major axis horizontally. We introduced an x − y disk coordi- nate system with the star at the origin and the +x coordinate along the derived disk major axis in WNW direction and the y a coordinate perpendicular to this with the positive axis toward NNE (θ = 22◦) as shown in Fig. 2(b).
The observed Qϕ flux image shows areas of enhanced sur- face brightness at the separations |x| ' 0.1 − 0.300 but located about 0.0400 above the x-axis and this up-down asymmetry is reflected clearly in the surface brightness contours shown in b Fig. 2(b). Figure 3 shows the profile for the polarized flux along the x-axis measured in bins of ∆x = 29 mas and integrated in the y-direction from y = −0.1300 to y = +0.1600. Our data show a higher flux closer to the star with a maximum flux inside r = 0.300 and two small brightness peaks at |x| ≈ 0.300 (8.5 au) indicated with arrows "A" and "B" in Figs. 2(b) and 3. c Figure 3 also includes background profiles determined be- 0.2’’ low and above the disk major axis by summing up the counts from y = −0.4200 to y = −0.1300 (light green dotted line) and 6 AU from y = +0.1600 to y = +0.4500 (green solid line). The disk flux is at least twice as high as the background, except for a small region around x ≈ +0.2300 where the background is par- ticularly high. The origin of the enhanced background below the disk midplane is unclear. The errors on flux per bin were Fig. 4. Comparison of the grid model with the Qϕ image. (a): Qϕ calculated from the variance of the sum of pixel values in bins image after 8x8 binning. (b): Image of the best-fitting grid model assuming a sample of normal random variables. The uncer- convolved with the instrumental PSF. (c): Residual image obtained after subtraction of the PSF-convolved grid model image (b) from tainty of the pixel value is given by the standard deviation of the Q image (a). Color bar shows flux in counts per binned pixel. the flux distribution (counts per pixel) computed in concen- ϕ tric annuli in the Qϕ image (excluding the area containing the disk flux) to take into account the radial dependence of the data variance. As an additional noise estimator, we measured the background in the Uϕ image (black solid line in Fig. 3) in the same areas where the polarized flux of the disk was mea- disk is detected up to a radial distance of r ∼ 0.800. Beyond 00 sured in the Qϕ image. The polarized scattered light from the r = 0.3 , the polarized flux per x-bin is less than 8 ct/s.
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Table 2. Disk model parameters.
Grid model MCMC model Optimized parameter 2 Range Step Min χν Mean value Range Best-fit value +1.5 Position angle θdisk, deg (...) (...) (...) (...) [109, 114] 112.3−1.5 +0.06 +1.7 +0.06 +1.7 Radius of ’belt’ r0, arcsec (au) [0.21, 0.42] 0.0175 0.38 0.36−0.06 10.3−1.7 [0.25, 0.50] 0.40−0.06 11.3−1.7 +0.04 +1.23 +0.01 +0.3 Scale height H0, arcsec (au) [0.00, 0.1] 0.02 0.04 0.05−0.04 1.36−1.23 [0.00, 0.1] 0.02−0.01 0.6−0.3 +3.3 +0.8 Inner radial index αin [0, 6] 1 3 3.5−3.3 [0, 6] 2.3−0.6 +5.7 +2.5 Outer radial index αout [-11, 0] 1 -7 -6.8−5.7 [-20, 0] -9.8−4.1 +2.75 +0.4 Flare index β [0.25, 1.50] 0.25 0.25 0.45−2.75 [0.0, 1.0] 0.4−0.3 +8.2 +1.7 Inclination i, deg [96, 111] 1 105 103.5−8.2 [96, 111] 103.8−1.7 +0.38 +0.08 HG parameter gsca [0.2, 1.0] 0.1 0.6 0.64−0.38 [0.2, 1.0] 0.74−0.10 +12.36 +0.8 Scaling factor Ap (...) (...) 1.1 0.9−12.36 (...) 2.8−0.9
5.2. Modeling the observed disk flux ing cross section per particle is a free parameter included in the scaling factor A . We modeled the spatial distribution of dust in HD 172555 disk p The Qϕ model image is calculated from the combination with the 3D single scattering code presented in Engler et al. of the PSF convolved images of the Stokes parameters Q and (2017). The disk geometry is described by a radius r0, where U. The individual steps of the modeling procedure are de- the radial distribution of the grain number density has a max- scribed and illustrated in Appendix A. imum, and by inner and outer radial power-law falloffs with To find parameters of the model that best fits the Qϕ image exponents αin and αout, respectively. For the vertical distri- (Fig. 4a), we took a twofold approach: first, we fitted the data bution we adopt the simpler Lorentzian profile instead of the with models drawn from a parameter grid and second we used exponential profile. The former profile has already been used the Markov chain Monte Carlo (MCMC) technique. for this purpose (e.g., Krist et al. 2005) and has an advantage that it is described with one parameter less. The Lorentzian profile is given by 5.2.1. Grid of models 4 !2−1 We define an extensive parameter grid of ∼10 models and h calculate a synthetic Qϕ image for each model. The explored fL(h) = aL1 + , H(r) parameter space and steps of linear sampling are given in Ta- ble 2, Cols. 2 and 3. In this first modeling approach, the disk ◦ where h is the height above the disk midplane and aL is the PA is set to θdisk = 112 , which is the PA value found in peak number density of grains in the disk midplane. The the previous section (Sect. 5.1). The flux scaling factor Ap scale height of the disk H(r) is defined as a half width at is treated as a free parameter for each model and is obtained 2 half maximum of the vertical profile at radial distance r and by minimizing the χ for the fit of the Qϕ model image to the scales as in H(r) = H (r/r )β. 2 0 0 data. The reduced χν metric is estimated as follows:
2 The parameters of the model are the PA of the disk θdisk, N h i 1 Xdata Fi, data − Ap · Fi, model(p) the radius of the planetesimal belt r0, inner αin and outer αout χ2 = , (1) ν ν 2 power law exponents, scale height H0, flare exponent β, in- i=1 σi, data clination angle i, Henyey-Greenstein (HG) scattering asym- metry parameter gsca and the scaling factor Ap. The scattering where Ndata is a number of pixels used to fit the data, Fi, data is phase function for the polarized flux fp (θ, gsca) is the prod- the flux measured in pixel i with an uncertainty σi, data, and uct fp (θ, gsca) = HG(θ, gsca) · pRay(θ) of the HG function and Fi, model(p) is the modeled flux of the same pixel. The de- the Rayleigh scattering function (see Fig. 8 in Engler et al. gree of freedom of the fit is denoted by ν = Ndata − Npar, (2017)). where Npar represents the number of model parameters p =
We assume that the debris disk is optically thin and ne- (p1, p2, ..., pNrmpar ). glect multiple scattering. The HG parameter has only positive To be less affected by single pixel noise and to speed up values (0 6 gsca 6 1) assuming that the dust particles are pre- this procedure, we reduce the number of pixels of the original dominately forward-scattering as inferred from imaging po- Qϕ image (Fig. 2(a)) by 8 × 8 binning and select a rectangular larimetry of other highly inclined debris disks (e.g., Olofsson image fitting area with a length of 63 and width of 19 binned et al. 2016; Engler et al. 2017). This means that the brighter pixels (1.8300 × 0.5500; Fig. 4(a)) centered on the star. A round side of the disk is the near side and the inclination higher than area with radius of 2.5 binned pixels covering the coronagraph 90◦ defines a disk with its near side toward north as in the case and a few pixels around this region are excluded from the of the HD 172555 disk. fitting procedure. 2 To simplify the model computation, we adopt the same The minimum χν = 1.17 is achieved for the model with grain properties everywhere in the disk. The average scatter- parameters listed in Col. 4 of Table 2. Considering all the
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2 models that fit the observations well and have a χν < 2, we Also, the radial profiles for the polarized flux of both mod- derive the parameter distribution and fit a Gaussian for each els, which are calculated in the same bins as in the Qϕ image model parameter (see Fig. C.1). We adopt the mean values of (Fig. 4(a)), are qualitatively very similar (cf. yellow solid and the parameter distribution as the best-fitting model presented dotted lines in Fig. 3a). in Col. 5 of Table 2. The errors on the mean parameters are given by the 68 % confidence interval derived for the respec- tive distribution. 5.2.4. Modeling cancellation effect The synthetic image of the best-fitting model (Fig. 4(b)) is 5.2.2. MCMC modeling important for a correction of the polarized flux due to the extended instrument PSF. One effect is the loss of polariza- We use the parameters of the best-fitting model from the pa- tion signal because parts of it are outside the flux integration rameter grid (Sect. 5.2.1) as a starting point for the MCMC aperture. The second and more important effect for compact run. To perform this analysis, we employed the Python mod- sources is the polarization cancellation effect where the posi- ule emcee by Foreman-Mackey et al. (2013), which imple- tive and negative Q flux features in the Stokes Q image, and ments affine invariant MCMC sampler suggested by Good- similar for Stokes U, cancel each other substantially if their man & Weare (2010). The uniform priors are defined as spec- separation is not much larger than the PSF. As described in ified in Col. 6 of Table 2. Contrary to the modeling with a grid Schmid et al. (2006) and Avenhaus et al. (2014), this can eas- of parameters (Sect. 5.2.1), the PA θdisk is allowed to vary. ily cause a reduction of the measurable polarization flux by a For the run of the standard ensemble sampler, 1000 walk- factor of two or more, depending on the source geometry and ers are initialized to perform a random walk with 2000 PSF structure. steps. The posterior distributions of the parameters shown We determine the total polarized flux for our best-fit in Fig. C.2 are obtained discarding the burn-in phase of 400 model before and after convolution with the instrument PSF walker steps. The mean fraction of the accepted steps within and derive for the cancellation effect a factor of 0.61 for our the chain is 0.342 and the maximum autocorrelation time of observations of the HD 172555 debris disk. In addition we parameter samples is 90 steps. This indicates a good conver- find that only 82 % of the polarized flux of the convolved gence and stability of the chain by the end of the MCMC run images fall into the rectangular disk-flux measuring areas in- (Foreman-Mackey et al. 2013). dicated by the white corners in Fig. 2, while 4 % of the flux is A set of the most probable parameters, which are consid- covered by the coronagraphic mask near the star and 14 % of ered to be the parameters of the best-fitting MCMC model, is the polarized flux are distributed in a very low surface bright- listed in Col. 7 of Table 2. These parameters are derived as the ness halo further out. 50th percentile of the posterior distribution. Their lower and upper uncertainties are quoted based on the 16th and 84th per- centiles of the samples, respectively. Figure C.2 demonstrates 5.3. Measured polarized flux contrast of the disk the degeneracy between some of the model parameters, for To compare the polarized flux from the disk with the stellar instance, between HG parameter gsca and inclination of the flux we first derive the expected count rates of the star in the disk i or scale height H0. coronagraphic image, if there were no coronagraph hiding its PSF peak. This is obtained with the flux frames where the 5.2.3. Modeling results star is offset from the coronagraphic mask. We use two flux measurements from the nights when we obtained good results The MCMC sampling result for the PA of the disk is essen- (177 and 249) and derive a mean count rate for the central star tially the same as the PA we found by subtracting one disk of (4.36 ± 0.08) · 105 counts per second (ct/s) per ZIMPOL side from the other (Sect. 5.1). Regarding other parameters, arm by summing up all counts registered within the aperture the best-fitting grid model (Table 2 Col. 5) and the MCMC with a radius of 1.500 (413 pixels). Then we correct with a model (Table 2 Col. 7) are consistent with each other. They factor of 1.007 for the coronagraph attenuation at a distance 00 indicate a disk radius r0 between 10 and 12 au and a disk in- of 0.35 from the stellar PSF peak and a factor of ∼115 to clination of ≈103.5◦. The scale height of the vertical profile account for the mean transmission of the neutral density filter H0 is 10 to 20 times smaller than the radius of the disk. Ac- ND2.0 in the VBB filter. We obtain an average count rate of cording to the MCMC model, the outer density falloff is at (5.00 ± 0.14) · 107 ct/s per ZIMPOL arm for the expected flux least steeper than about αout = −7. It is not clear whether the of the central star for observation in the fast polarimetry mode disk is cleared inside r0 because the inner radial index αin is with the pupil mask but without correction for the attenuation smaller than 3. Both models indicate a relatively high asym- by the focal plane mask or ND2.0 filter. metry parameter for scattering gsca ≈ 0.7. This result could For the disk, we derive the total polarized flux by sum- be affected by a higher surface brightness, which we observe 00 ming up all the counts in two rectangular areas indicated with inside r = 0.2 . The flare index β is the only parameter that white brackets in Fig. 2(a), from |x| = 0.0800 to 0.7700 along remains unconstrained in both modeling methods (grid and the major axis and from y = −0.1300 to 0.1600 perpendicular to MCMC) showing a tendency to be 0. it. The innermost regions with radial separations |x| < 0.0800 Both models fit the Qϕ image equally well according to are largely hidden behind the coronagraphic mask, and there- 2 2 the χν metric: the grid model has a χν = 1.20 (ν = 1152) and fore they are not included in this estimate. The total polarized 2 the MCMC model has a χν = 1.19 (ν = 1151). The residual flux in the VBB filter after the modulation-demodulation images of both models show no noticeable differences. There- efficiency calibration amounts to 780 ± 150 (ESE side, left) fore, in Fig. 4, we show only the grid model in comparison to and 760 ± 150 (WNW side, right) ct/s and per ZIMPOL arm. the Qϕ image. Therefore, the total net flux obtained by integrating over
Article number, page 8 of 16 Engler et al.: HD 172555 hot debris disk
Fig. 5. Photometry of the star and disk together with the blackbody SED fits. abovementioned areas is 1540 ± 300 ct/s per ZIMPOL arm. mode. For HD 172555 we derive a magnitude m(VBB) = 4.68m ± 0.03m (indicated with a black asterisk in Fig. 5). This measured flux must still be corrected for the polari- This value is in good agreement with the Johnson photomet- metric cancellation effects to get a value for the intrinsic po- ric magnitude in R band m(R) = 4.887m ± 0.023m and I band larized flux. Because of the limited spatial resolution of our m(I) = 4.581m ± 0.025m (Johnson et al. 1966). data, the polarization in the positive and negative Q regions is For the estimated above ratio of the disk total polarized −5 reduced since signals with opposite signs overlap and cancel flux to stellar flux (Fpol)disk/F∗ > (6.2 ± 0.6) · 10 , disk mag- m m each other. We quantified this effect and calculated correction nitude in the VBB filter is mpdisk(VBB) = 15.20 ± 0.37 (in- factors using our best-fit model (see description in the last dicated with a blue asterisk in Fig. 5). paragraph of Sect. 5.2). At radial separation of r ≈ 0.300 indicated with arrows Taking into account the PDI efficiency, which causes the "A" and "B" in Figs. 2(b) and 3, the peak surface brightness reduction of disk polarized flux by a factor of ∼1.7 and cor- is ∼15 ct/s per binned pixel (0.02900 × 0.02900) and corre- m m −2 rection factor for the aperture size (see Sect. 5.2), the total sponds to the SBpeak(VBB) = 13.3 ±0.3 arcsec or surface polarized flux of the disk is at least twice as large as the brightness contrast for the polarized flux of SBpeak(VBB) − −2 total net flux and is equal to 3100 ± 600 ct/s per ZIMPOL mstar(VBB) = 8.62 mag arcsec . arm. This flux corresponds to the intrinsic modeled polar- ized flux compatible with our observation. With this value, the lower limit for the ratio of the disk total polarized flux to 6. Discussion −5 the stellar flux is (Fpol)disk/F∗ > (6.2 ± 0.6) · 10 (cf. with 6.1. Comparison with thermal light detection and −5 the ratio (Fpol)disk/F∗ = 3.1 · 10 obtained for the net flux interferometry (F ) = 1540 ct/s). pol disk The disk geometry is consistent with the 18 µm image pre- sented in Smith et al. (2012). They found two lobes of ex- 5.4. Polarimetric flux tended emission along PA = 110◦ with a separation of about 0.400 from the star and a flux of 105 mJy. On top of this, To check our photometry, we compare the measured stellar they measured a roughly seven times stronger (732 mJy) un- flux with the stellar magnitudes from the literature. The stellar resolved dust component and a stellar flux of 202 mJy. In count rate of (4.36 ± 0.08) · 105 ct/s per ZIMPOL arm before the N-band image the dust was not resolved by Smith et al. correction for the transmission of the neutral density filter can (2012), but their N-band MIDI interferometry resolved the be converted to the photometric magnitude m(VBB) (Schmid dust fully, putting it at separations between > 0.03500 and et al. 2017) as follows: < 0.2700 (1 − 8 au). Therefore, we also expect that a lot of polarized light from the dust scattering contributes to the sig- m(VBB) = −2.5 log(ct/s)−am·k1(VBB)−mmode+zpima(VBB), nal inside the inner working angle of the SPHERE/ZIMPOL m 00 where am = 1.3 is the airmass, k1(VBB) = 0.086 is the fil- observations at 0.12 , which cannot be measured. ter coefficient for the atmospheric extinction, zpima(VBB) = The disk modeling of the infrared flux by Smith et al. 24.61m is the photometric zero point for the VBB filter, and (2012) yields a disk with radius r = 0.2700 and width dr = m mmode = 5.64 is an offset to the zero point, which accounts 1.2r, which is equivalent to the ring with constant surface for the instrument configuration, pupil stop (STOP1_2), neu- brightness between 0.100 and 0.400, inclined at 75◦ to the line tral density filter ND2.0, and the fast polarimetry detector of sight and at PA= 120◦ for the disk major axis. We confirm
Article number, page 9 of 16 A&A proofs: manuscript no. HD172555_v7_arxiv these parameters with our observation and can provide more Table 3. Photometry of HD 172555. stringent parameters for the inclination and the disk orienta- tion because of the higher spatial resolution of our data. Also Filter Wavelength Flux density Error Ref. the disk extension agrees, but it is not clear whether the scat- (µm) (Jy) (Jy) tered light emission and thermal emission should show the Johnson B 0.44 53.87 0.94 1 same radial flux distributions. In Fig. 5, we compare the flux distribution λFλ from the Johnson V 0.55 38.45 0.53 1 stellar photosphere with the thermal emission of the disk and Johnson R 0.7 33.40 0.71 1 the polarized flux distribution measured in this work. Photo- metric data points of HD 172555 are listed in Table 3 and Johnson I 0.9 35.74 0.82 1 plotted as green diamonds in Fig. 5, which also includes a Si-5 (N) 11.7 1.120 0.067 2 S pitzer/IRS spectrum1. The stellar spectral flux density is ap- proximated by a Planck function for the star temperature of Qa (Q) 18.3 1.039 0.085 2 7800 K (Riviere-Marichalar et al. 2012). A black asterisk (la- PACS70 70 0.191 0.005 3 beled VBB) denotes the stellar magnitude measured in the PACS100 100 0.089 0.003 3 VBB (this work). The near-IR aperture photometry of HD 172555 in the N and Q bands (green diamonds at 11.7 and PACS160 160 0.036 0.02 3 18.3 µm), performed by Smith et al. (2012) using TReCS imaging data, is indicated by capital letters ‘N’ and ‘Q’. The thermal flux from the disk is shown as a blackbody emission References. (1) Johnson et al. (1966); (2) Smith et al. with the temperature of 329 K found by Riviere-Marichalar (2012); (3) Riviere-Marichalar et al. (2012). et al. (2012) (orange solid line). The net polarized flux mea- sured in the Qϕ image (Sect. 5.3) is indicated by a light blue asterisk (labeled with ’I = Q ’), and the polarized flux pol ϕ pact disk. Then, there is another factor 2.67 between the total corrected for the polarimetric cancellation effects and aper- convolved polarized flux from the disk and the convolved po- ture size is indicated by a blue asterisk in this figure. The larized flux that falls into the rectangular measuring areas of blue dotted line shows an approximate curve for the SED of our observations shown in Fig. 2(a) because a major region of the polarized light obtained by scaling down the SED of the the polarization signal is hidden by the coronagraphic mask. star. Using our best-fitting grid model we roughly estimated Thus, only about 15 % of the polarized flux produced by an the scattered flux from the disk (averaged over full solid an- inner compact disk would contribute to our measurement. We gle) in the VBB filter. This conversion neglects the contri- measure a net flux of 1540 ct/s in the measuring area of our bution from the diffracted light and assumes that the maxi- observation and estimate that it is not possible to recognize mum polarization fraction of the phase function for the polar- an inner disk in our data, which contributes less than 150 ct/s ized flux is p = 0.3. This value is denoted with a yel- max to our measurement. Thus, an unseen compact disk with the low asterisk and labeled ’’. We used this magnitude sca geometry as described above and an intrinsic polarized flux as a proxy for the scattered flux of the disk to compare it of 6.675 x 150 ct/s could be present without being in conflict with the maximum thermal flux of the disk at λ = 10 µm with our observations and even more scattered light could be and thus to estimate a kind of the disk albedo. We obtain hidden for a more compact inner disk.
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N E
0.1 ’’
1 4 7 10 -0.5 0.5 1.5 2.5 -0.8 -0.4 0 0.4 0.8
Fig. 6. Model of the small debris disk that could be hidden behind the coronagraphic mask. The model parameters correspond to those of the mean model (Table 2) except the radius of the belt and scale height of the dust vertical distribution, which are reduced by a factor of 5. (a) Qϕ image of the debris disk model showing the polarized intensity before being convolved with the instrumental PSF. (b) Qϕ image of the debris disk model showing the polarized intensity after convolution with the instrumental PSF. The black circle denotes the edge of the coronagraphic mask. (c) Uϕ image of the model demonstrating nonzero Uϕ signal appearing after convolution of the Stokes Q and U parameters with the instrumental PSF. The color bars show counts per pixel.
filter using differential polarimetry. We found that the ob- from 0.3000 to 0.4500 and overlaps the region of interest. In the served polarized intensity is consistent with an axisymmetric I band, the speckle ring is further outside of ∼ 0.4000 and the dust distribution, which can be interpreted as a parent belt of achievable contrast is higher under optimal observing condi- planetesimals or disk with a radius in the range between 0.300 tions even if the amount of photons received in the I band is (8.5 au) and 0.400 (11.3 au). We analysed the disk structure a factor of 0.6 lower than in the VBB. Moreover, noncoro- and obtained the following results: nagraphic data taken with I band are more suitable for the ◦ ◦ measurement of the beam shift between the two orthogonal – The PA for the disk major axis is θdisk = 112.3 ± 1.5 on polarization states and, hence, the correction of the beamshift the sky. effect (Schmid et al. 2018, submitted) is much easier. Such – The disk emission is slightly shifted in NNE direction observation may also allow us to probe the innermost dust in from the star indicating that the front side or forward- the HD 172555 system. scattering part of the disk is on the NNE side. The ob- served dust distribution can be described with the HG Acknowledgements. We would like to thank the referee for many thoughtful comments that helped to improve this paper. This work is supported by the asymmetry parameter g ≈ 0.7 and disk inclination ≈ Swiss National Science Foundation through grant number 200020 - 162630. 103.5◦. – Data analysis and modeling results do not suggest the clearing of the inner disk regions (inside r = 0.300). – The total disk magnitude in polarized flux in the VBB fil- References m m ter is mpdisk(VBB) = 15.20 ± 0.37 and the stellar flux is m m Avenhaus, H., Quanz, S. P., Meyer, M. R., et al. 2014, ApJ, 790, 56 m(VBB) = 4.68 ±0.03 . This gives a disk to star contrast Beuzit, J.-L., Feldt, M., Dohlen, K., et al. 2008, in Proc. SPIE, Vol. 7014, −5 (Fpol)disk/F∗ of (6.2 ± 0.6) · 10 . The measured peak sur- Ground-based and Airborne Instrumentation for Astronomy II, 701418 face brightness of the polarized light is SBpeak(VBB) = Bonnefoy, M., Milli, J., Ménard, F., et al. 2017, A&A, 597, L7 m ± m −2 Chen, C. H., Mamajek, E. E., Bitner, M. A., et al. 2011, ApJ, 738, 122 13.3 0.3 arcsec . This corresponds to a surface Chen, C. H., Sargent, B. A., Bohac, C., et al. 2006, ApJS, 166, 351 brightness contrast of SBpeak(VBB) − mstar(VBB) = 8.62 Choquet, É., Perrin, M. D., Chen, C. H., et al. 2016, ApJ, 817, L2 mag arcsec−2. Cote, J. 1987, A&A, 181, 77 – When compared with the fractional infrared luminosity Dohlen, K., Beuzit, J.-L., Feldt, M., et al. 2006, in Proc. SPIE, Vol. 6269, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference of the disk using the Λ parameter, the fractional polarized Series, 62690Q light flux in the VBB filter makes up ∼ 9%. Engler, N., Schmid, H. M., Thalmann, C., et al. 2017, A&A, 607, A90 Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, Our data demonstrate high sensitivity and ability of ZIMPOL 125, 306 to resolve the polarized light from the hot debris around a Fujiwara, H., Ishihara, D., Kataza, H., et al. 2009, in Astronomical Society of nearby A star as close as 0.100 or ∼3 au. It would be worth re- the Pacific Conference Series, Vol. 418, AKARI, a Light to Illuminate the observing HD172555 in the I band without the coronagraph. Misty Universe, ed. T. Onaka, G. J. White, T. Nakagawa, & I. Yamamura, 109 Additional observations of this target under excellent observ- Fusco, T., Sauvage, J.-F., Petit, C., et al. 2014, in Proc. SPIE, Vol. 9148, ing conditions, i.e., seeing 6 0.7, airmass 6 1.4, coherence Adaptive Optics Systems IV, 91481U time > 3.5 ms, and wind speed > 3 m/s, to avoid the low wind Gaia Collaboration. 2016, VizieR Online Data Catalog, 1337 effect (see SPHERE Manual) and with different offsets of the Goodman, J. & Weare, J. 2010, Comm. App. Math. Comp. Sci.„ 5, 65 Grady, C. A., Brown, A., Welsh, B., et al. 2018, AJ, 155, 242 sky field on the detector would allow us to better distinguish Gray, R. O., Corbally, C. J., Garrison, R. F., et al. 2006, AJ, 132, 161 between the instrumental features in the PSF and the real as- Høg, E., Fabricius, C., Makarov, V. V., et al. 2000, A&A, 355, L27 trophysical signal. In the VBB filter the speckle ring extends Johnson, B. C., Lisse, C. M., Chen, C. H., et al. 2012, ApJ, 761, 45
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Johnson, H. L., Mitchell, R. I., Iriarte, B., & Wisniewski, W. Z. 1966, Com- Appendix A: Modeling the Qϕ and Uϕ images munications of the Lunar and Planetary Laboratory, 4, 99 Kasper, M., Beuzit, J.-L., Feldt, M., et al. 2012, The Messenger, 149, 17 Figure A.1 simulates the polarized flux measurement with the Kiefer, F., Lecavelier des Etangs, A., Augereau, J.-C., et al. 2014, A&A, 561, ZIMPOL instrument. In the first step, the distribution of the L10 dust number density in the disk is generated using the pa- Krist, J. E., Ardila, D. R., Golimowski, D. A., et al. 2005, AJ, 129, 1008 Lisse, C. M., Chen, C. H., Wyatt, M. C., et al. 2009, ApJ, 701, 2019 rameters of the mean model. Then, synthetic images of debris Maire, A.-L., Langlois, M., Dohlen, K., et al. 2016, in Proc. SPIE, Vol. 9908, disk in polarized light are calculated assuming only the single Ground-based and Airborne Instrumentation for Astronomy VI, 990834 scattering of photons. An image of the polarized imtensity, or Mamajek, E. E. & Bell, C. P. M. 2014, MNRAS, 445, 2169 Qϕ image (Fig. A.1 (a)), is obtained considering angular de- Matthews, B. C., Krivov, A. V., Wyatt, M. C., Bryden, G., & Eiroa, C. 2014, pendence of polarization fraction on scattering angle θ such Protostars and Planets VI, 521 Mittal, T., Chen, C. H., Jang-Condell, H., et al. 2015, ApJ, 798, 87 as that for Rayleigh scattering. Single scattering of photons Moerchen, M. M., Telesco, C. M., & Packham, C. 2010, ApJ, 723, 1418 produces linearly polarized light oriented perpendicular to the Moór, A., Ábrahám, P., Derekas, A., et al. 2006, ApJ, 644, 525 scattering plane, which corresponds to the azimuthal orienta- Morales, F. Y., Rieke, G. H., Werner, M. W., et al. 2011, ApJ, 730, L29 tion of electric field in the 2D Q image. The U image (Fig. Olofsson, J., Samland, M., Avenhaus, H., et al. 2016, A&A, 591, A108 ϕ ϕ A.1 (b)) displays no signal because the Stokes Uϕ parameter Riviere-Marichalar, P., Barrado, D., Augereau, J.-C., et al. 2012, A&A, 546, ◦ L8 should show the polarization component in direction at 45 to Schmid, H. M., Bazzon, A., Milli, J., et al. 2017, A&A, 602, A53 the azimuthal direction. In this direction we do not expect to Schmid, H. M., Joos, F., & Tschan, D. 2006, A&A, 452, 657 measure any signal if the assumption of single scattering is Schneider, G., Grady, C. A., Hines, D. C., et al. 2014, AJ, 148, 59 valid. Schütz, O., Meeus, G., & Sterzik, M. F. 2005, A&A, 431, 175 Smith, R., Wyatt, M. C., & Haniff, C. A. 2012, MNRAS, 422, 2560 In the following step, the Stokes Q and U images are cal- Torres, C. A. O., Quast, G. R., da Silva, L., et al. 2006, A&A, 460, 695 culated using the coordinate transformation Trilling, D. E., Bryden, G., Beichman, C. A., et al. 2008, ApJ, 674, 1086 Wilson, T. L., Nilsson, R., Chen, C. H., et al. 2016, ApJ, 826, 165 Q = −Qϕ cos 2ϕ (A.1) Wyatt, M. C. 2008, ARA&A, 46, 339 Wyatt, M. C., Smith, R., Greaves, J. S., et al. 2007a, ApJ, 658, 569 Wyatt, M. C., Smith, R., Su, K. Y. L., et al. 2007b, ApJ, 663, 365 U = −Qϕ sin 2ϕ, (A.2) where ϕ is the polar angle of each image point and is mea- sured from NoE. This polar coordinate system corresponds to the measurement axes of the instrument shown on the right side of Fig. A.1. In ZIMPOL, the Stokes Q+ parameter is mea- sured along north-south axis and the Stokes U+ parameter is measured along northeast-southwest axis. The Q and U images (Figs. A.1 (c) and (d)) are em- ployed to create the images of individual polarization states I0, I45, I90, and I135. These images are firstly convolved with the PSF measured from the HD 172555 data and then are utilized to calculate new images of the Q and U parameters again but now in convolved state (Figs. A.1 (e) and (f)). These two images imitate the output of the ZIMPOL data reduction pipeline. Usually they are used to compute the final Qϕ and Uϕ images of the disk applying reverse coordinate transfor- mation as follows:
Qϕ = −(Q cos 2ϕ + U sin 2ϕ), (A.3)
Uϕ = −Q sin 2ϕ + U cos 2ϕ. (A.4)
Examination of the final Qϕ and Uϕ images (Figs. A.1 (g) and (h)) leads to two important conclusions. Comparison of the unconvolved and convolved Qϕ images (Figs. A.1 (a) and (g)) demonstrates the loss of a fraction of the polarized flux due to the convolution of the intensity of two orthogonal po- larization states with the instrumental PSF (see also Sect. 5.2). As a result of blurring effect on the positive and negative sig- nals in the Stokes Q and U due to the convolution with PSF, a nonzero signal is present in the final Uϕ image (Fig. A.1 (h)). For the mean model shown in Fig. A.1, the generated Uϕ flux is of one order smaller than the Qϕ flux that we measure in the Qϕ image (Fig. A.1 (g)). In general, this artificially created Uϕ flux and the magnitude of the flux loss in the Qϕ image depend on the geometry and extent of the polarized flux source and on the PSF structure. For the small compact sources, the gener- ated Uϕ flux and the PDI efficiency loss are the largest because
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a c e g + U N + E Q Q-
U- W S
b d f h
Fig. A.1. Model images of the polarized flux from HD 172555 debris disk. Images were generated using the parameters of mean model (Col. 5 in Table 2) and illustrate the individual steps of the modeling procedure (from left to the right) to obtain the final synthetic Qϕ and Uϕ images ((g) and (h)). For a detailed description of the presented images, see Appendix A. The diagram on the right side of the figure explains orientation of the axes used to measure the Stokes Q and U parameters as implemented in ZIMPOL instrument. The diagram shows also the orientation of north and east in each image. The north is rotated by 22◦ clockwise from the vertical line to have disk axis in horzontal position. Nonalignment of the disk axes with the Q and U measuring axes causes asymmetric flux distribution in Q and U images ((c), (d), (e), and (f)). the resolution of instrument is limited. Therefore, this effect Appendix B: HD 172555 polarimetric data per should be estimated by means of modeling for each individ- observing run ual object and detector. To demonstrate this point, we calcu- late two additional models with the same parameters and the Figure B.1 shows the reduced imaging data of HD 172555 same aspect ratio of radius of the planetesimal belt to scale from all six observing runs. The FITS files of the total height as in the mean model but with different radii of the intensity (Stokes I) and Stokes parameters Q and U of belts: one model with radius r = 2 au (0.0700) shown in Fig. the data presented in rows two and four in this figure are 6 and another model with the radius r = 30 au (1.0500). Our available in electronic form at the CDS via anonymous ftp results show that the total polarized flux of the smaller debris to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u- disk is reduced by a factor of 0.4, whereas the extended disk strasbg.fr/cgi-bin/qcat?J/A+A/. suffers much less from the convolution effect and reducing factor is 0.73 for this disk. Appendix C: Probability distributions for fitted parameters See Figures C.1 and C.2.
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Fig. B.1. Reduced imaging data of HD 172555 from all six observing runs arranged from top to the bottom with the Stokes I (left column), Q (middle column) and U (right column) data. Each run was carried out with fixed sky orientation on the CCD detector with PA offset indicated in parenthesis. The highest quality observations are in rows two and four. To get north up and east to the left, each image should be rotated by the PA off- arcsec set counterclockwise and the True North off- Stokes I flux (ct) Stokes Q / U flux (ct) set of the ZIMPOL should be taken into ac- count. The yellow lines in the Q and U im- ages show the position of disk major axis.
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2 Fig. C.1. One-dimensional marginalized distributions of model parameters drawn from the sample of well-fitting models (χν < 2). The red dotted lines denote Gaussian fits to the parameter distributions. Their mean values µ and standard deviation σ are given in brackets.
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Fig. C.2. One- and two-dimensional posterior probability distributions of the fitted parameters.
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